final exam due in 20 hours
combs
4320CorrelationPart1.pptxCorrelation
What is a Correlation?
Answers the question: “What is the relationship between A and B?”
Correlation coefficients: used to quantitatively describe the strength and direction of a relationship between 2 variables.
Independent variable
Catagorical (nominal or ordinal)
Numerical (interval or ratio)
Dependent variable
Catagorical (nominal or ordinal)
Numerical (interval or ratio)
Question: Is there a Relationship?
In Summary
Correlations are performed between two dependent variables
The one listed as the independent variable is typically the one you expect to be affecting the other. It becomes the x axis variable
In reality either variable may be the independent variable.
Examples
Is there a relationship between IQ and ACT scores?
Independent
Most would assume IQ
Dependent
ACT by default
Switching only changes the axis-does not change the results.
Where does “Correlation” come from?
A correlation exists if a person varies on one variable in a similar way that he/she varies on another variable.
Covariance: is a measure of how much two variables change together
Co-relation is all about “covariance” – that is, individuals vary consistently on variables
No Audio
Positive Correlation–as x increases, y increases
x = SAT score
y = GPA
GPA
Scatter Plots and Types of Correlation
4.00
3.75
3.50
3.00
2.75
2.50
2.25
2.00
1.50
1.75
3.25
300
350
400
450
500
550
600
650
700
750
800
Math SAT
Negative Correlation–as x increases, y decreases
x = hours of training
y = number of accidents
Scatter Plots and Types of Correlation
60
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
Hours of Training
Accidents
No linear correlation
x = height y = IQ
Scatter Plots and Types of Correlation
160
150
140
130
120
110
100
90
80
60
64
68
72
76
80
Height
IQ
Correlation Coefficient “r”
A correlation coefficient indicates the extent to which two variables are related.
It can range from -1.0 to +1.0
A positive correlation coefficient indicates a positive relationship, a negative coefficient indicates an inverse relationship
Correlation CANNOT be equated with causality.
No Audio
What r is...
r is a measure of LINEAR ASSOCIATION
The closer r is to –1 or 1, the more tightly the points on the scatterplot are clustered around a line
The sign of r (+ or -) is the same as the sign of the slope of the line
When r = 0, the points are not LINEARLY ASSOCIATED – this does NOT mean there is NO ASSOCIATION
No Audio
“r”
r = 1.0
r = -1.0
“r”
r = .95
r = -.95
“r”
r = 0
r 0: curved relation
r 0: outliers
outliers
r 0: parallel lines
r 0: different linear trends
r 0: random scatter
...and what r is not
r is a measure of LINEAR ASSOCIATION
r does NOT tell us if Y is a function of X
r does NOT tell us if X causes Y
r does NOT tell us if Y causes X
r does NOT tell us what the scatterplot looks like
No Audio
Correlation Coefficient Interpretation
| Coefficient Range | Strength of Relationship |
| 0.00 - 0.20 | Very Low |
| 0.20 - 0.40 | Low |
| 0.40 - 0.60 | Moderate |
| 0.60 - 0.80 | High Moderate |
| 0.80 - 1.00 | Very High |
0
20
40
60
80
100
120
140
160
020406080100120140160
0
20
40
60
80
100
120
140
160
020406080100120140160
Chart1
| 10 |
| 15 |
| 20 |
| 25 |
| 30 |
| 35 |
| 40 |
| 45 |
| 50 |
| 55 |
| 60 |
| 65 |
| 70 |
| 75 |
| 80 |
| 85 |
| 90 |
| 95 |
| 100 |
| 105 |
| 110 |
| 115 |
| 120 |
| 125 |
| 130 |
| 135 |
| 140 |
| 145 |
| 150 |
Sheet1
| Assignment Scores | Final Examination Scores |
| 10 | 10 |
| 15 | 15 |
| 20 | 20 |
| 25 | 25 |
| 30 | 30 |
| 35 | 35 |
| 40 | 40 |
| 45 | 45 |
| 50 | 50 |
| 55 | 55 |
| 60 | 60 |
| 65 | 65 |
| 70 | 70 |
| 75 | 75 |
| 80 | 80 |
| 85 | 85 |
| 90 | 90 |
| 95 | 95 |
| 100 | 100 |
| 105 | 105 |
| 110 | 110 |
| 115 | 115 |
| 120 | 120 |
| 125 | 125 |
| 130 | 130 |
| 135 | 135 |
| 140 | 140 |
| 145 | 145 |
| 150 | 150 |
Sheet2
Sheet3
Chart1
| 10 |
| 15 |
| 20 |
| 25 |
| 30 |
| 35 |
| 40 |
| 45 |
| 50 |
| 55 |
| 60 |
| 65 |
| 70 |
| 75 |
| 80 |
| 85 |
| 90 |
| 95 |
| 100 |
| 105 |
| 110 |
| 115 |
| 120 |
| 125 |
| 130 |
| 135 |
| 140 |
| 145 |
| 150 |
Sheet1
| Assignment Scores | Final Examination Scores |
| 10 | 150 |
| 15 | 145 |
| 20 | 140 |
| 25 | 135 |
| 30 | 130 |
| 35 | 125 |
| 40 | 120 |
| 45 | 115 |
| 50 | 110 |
| 55 | 105 |
| 60 | 100 |
| 65 | 95 |
| 70 | 90 |
| 75 | 85 |
| 80 | 80 |
| 85 | 75 |
| 90 | 70 |
| 95 | 65 |
| 100 | 60 |
| 105 | 55 |
| 110 | 50 |
| 115 | 45 |
| 120 | 40 |
| 125 | 35 |
| 130 | 30 |
| 135 | 25 |
| 140 | 20 |
| 145 | 15 |
| 150 | 10 |
Sheet2
Sheet3
0
20
40
60
80
100
120
140
160
180
200
020406080100120140160180200
0
20
40
60
80
100
120
140
160
180
200
020406080100120140160180200
Chart1
| 30.4964944235 |
| 38.2097567862 |
| 39.3612068811 |
| 47.7525892432 |
| 49.5187677632 |
| 45.158012134 |
| 58.1769784379 |
| 57.4450485302 |
| 59.1614252834 |
| 75.6975186983 |
| 86.6709461427 |
| 86.7018774721 |
| 80.4784630745 |
| 80.3256649551 |
| 89.695333998 |
| 99.215004159 |
| 101.8956557293 |
| 118.5747277459 |
| 123.7410023598 |
| 121.7239852792 |
| 122.5992369488 |
| 138.4458845283 |
| 138.3717625503 |
| 140.4198168966 |
| 144.3615519759 |
| 156.1417649491 |
| 159.6133749543 |
| 164.29523597 |
| 164.8522713252 |
Sheet1
| Assignment Scores | Final Examination Scores | |||
| 30.4964944235 | 171.8416404932 | 42.7496049193 | 179.8096301577 | |
| 38.2097567862 | 158.0910933765 | 50.8184653297 | 175.9441284069 | |
| 39.3612068811 | 153.9678605585 | 53.7143525668 | 172.8514342894 | |
| 47.7525892432 | 159.698354664 | 54.2229084782 | 179.5025063733 | |
| 49.5187677632 | 158.8809653584 | 58.7505139344 | 159.6814420245 | |
| 45.158012134 | 141.3005950822 | 54.3636999552 | 147.0084731074 | |
| 58.1769784379 | 124.4841119891 | 71.4636096717 | 125.7807375882 | |
| 57.4450485302 | 129.803654545 | 69.6769353889 | 148.1902036437 | |
| 59.1614252834 | 123.0310962518 | 72.7488040562 | 141.5563346102 | |
| 75.6975186983 | 119.7360992681 | 81.5709859991 | 120.3285563802 | |
| 86.6709461427 | 119.5707224829 | 94.2198474262 | 122.3185601536 | |
| 86.7018774721 | 115.4053149904 | 88.6879224354 | 126.1456186508 | |
| 80.4784630745 | 96.9383310744 | 89.6525875913 | 101.687119312 | |
| 80.3256649551 | 112.6892915433 | 83.6290841145 | 114.7651135531 | |
| 89.695333998 | 92.8720570426 | 96.8014386798 | 103.7465554376 | |
| 99.215004159 | 97.8120257129 | 112.4956242415 | 100.4873023121 | |
| 101.8956557293 | 83.2443367673 | 115.0920255224 | 101.3623569756 | |
| 118.5747277459 | 73.9712014714 | 124.3490051188 | 75.2742071949 | |
| 123.7410023598 | 72.509460919 | 137.145621494 | 73.5552106597 | |
| 121.7239852792 | 66.7554950171 | 132.7150428645 | 81.2902390036 | |
| 122.5992369488 | 57.0563729741 | 130.0023222326 | 67.0036046649 | |
| 138.4458845283 | 61.9787881564 | 148.3729963342 | 77.9677640849 | |
| 138.3717625503 | 45.0182943601 | 156.7633480252 | 56.9774277712 | |
| 140.4198168966 | 46.0087203597 | 148.4073059594 | 60.8844911813 | |
| 144.3615519759 | 42.982462211 | 153.7181777209 | 62.1542417031 | |
| 156.1417649491 | 52.1011838622 | 171.789746935 | 62.3741164713 | |
| 159.6133749543 | 27.0665204924 | 162.6709990034 | 41.7642148478 | |
| 164.29523597 | 31.6375658509 | 177.4475623078 | 41.920370126 | |
| 164.8522713252 | 23.8740321705 | 178.0757746925 | 35.521357511 |
Sheet2
Sheet3
Chart1
| 30.4964944235 |
| 38.2097567862 |
| 39.3612068811 |
| 47.7525892432 |
| 49.5187677632 |
| 45.158012134 |
| 58.1769784379 |
| 57.4450485302 |
| 59.1614252834 |
| 75.6975186983 |
| 86.6709461427 |
| 86.7018774721 |
| 80.4784630745 |
| 80.3256649551 |
| 89.695333998 |
| 99.215004159 |
| 101.8956557293 |
| 118.5747277459 |
| 123.7410023598 |
| 121.7239852792 |
| 122.5992369488 |
| 138.4458845283 |
| 138.3717625503 |
| 140.4198168966 |
| 144.3615519759 |
| 156.1417649491 |
| 159.6133749543 |
| 164.29523597 |
| 164.8522713252 |
Sheet1
| Assignment Scores | Final Examination Scores | |||
| 30.4964944235 | 23.8740321705 | 33.6956438029 | 33.7232453614 | |
| 38.2097567862 | 27.0665204924 | 50.5546732203 | 40.4158084796 | |
| 39.3612068811 | 31.6375658509 | 43.0120468877 | 39.2214280296 | |
| 47.7525892432 | 42.982462211 | 66.8788339538 | 48.3194590172 | |
| 49.5187677632 | 45.0182943601 | 52.5946102707 | 63.8904684018 | |
| 45.158012134 | 46.0087203597 | 57.2338187928 | 53.8565244516 | |
| 58.1769784379 | 52.1011838622 | 58.9007142481 | 69.6117112014 | |
| 57.4450485302 | 57.0563729741 | 69.4809805654 | 72.1719112201 | |
| 59.1614252834 | 61.9787881564 | 68.2764826253 | 75.9064428918 | |
| 75.6975186983 | 66.7554950171 | 78.9022128754 | 74.4791908841 | |
| 86.6709461427 | 72.509460919 | 104.198998855 | 91.1531104958 | |
| 86.7018774721 | 73.9712014714 | 93.9341051756 | 77.4802361323 | |
| 80.4784630745 | 83.2443367673 | 92.4132797915 | 89.7002807946 | |
| 80.3256649551 | 92.8720570426 | 96.3871820391 | 100.9248895779 | |
| 89.695333998 | 96.9383310744 | 94.0811562455 | 108.0332003608 | |
| 99.215004159 | 97.8120257129 | 116.6018372929 | 104.7498274022 | |
| 101.8956557293 | 112.6892915433 | 102.210403108 | 113.0662217425 | |
| 118.5747277459 | 115.4053149904 | 133.9352731801 | 121.4633407472 | |
| 123.7410023598 | 119.5707224829 | 123.8842515322 | 119.6682199653 | |
| 121.7239852792 | 119.7360992681 | 132.8006474805 | 121.485413058 | |
| 122.5992369488 | 123.0310962518 | 130.7252555145 | 127.2683667861 | |
| 138.4458845283 | 124.4841119891 | 148.3007583341 | 142.9445688247 | |
| 138.3717625503 | 129.803654545 | 147.3139492321 | 134.1767769365 | |
| 140.4198168966 | 141.3005950822 | 145.8617589337 | 153.9621421873 | |
| 144.3615519759 | 153.9678605585 | 153.9008379804 | 167.2485204851 | |
| 156.1417649491 | 158.0910933765 | 165.6961553666 | 171.6787726513 | |
| 159.6133749543 | 158.8809653584 | 177.5082054708 | 167.7056628315 | |
| 164.29523597 | 159.698354664 | 173.6522789187 | 171.2787781334 | |
| 164.8522713252 | 171.8416404932 | 184.5976101511 | 187.4070735831 |
Sheet2
Sheet3
0
20
40
60
80
100
020406080100
Chart1
| 97.872974135 |
| 99.5405692073 |
| 27.7298813345 |
| 16.7829198531 |
| 39.1476925049 |
| 7.9204401174 |
| 80.3250951219 |
| 33.4078497428 |
| 58.4901442099 |
| 52.8045522042 |
| 99.5698815727 |
| 65.1958848209 |
| 21.1551603571 |
| 59.5076038108 |
| 7.9486990725 |
| 14.2166604858 |
| 85.4351664029 |
| 38.1160643261 |
| 64.5214628819 |
| 48.6447111623 |
| 40.8351002516 |
| 29.081331575 |
| 50.7865490777 |
| 79.2706924588 |
| 44.5170424001 |
| 64.1540564077 |
| 44.3348210708 |
| 45.0269211468 |
| 9.9335520513 |
| 35.1070215713 |
Sheet1
| Assignment Scores | Final Examination Scores |
| 52.4440284781 | 96.867051352 |
| 6.9832960409 | 4.0831172033 |
| 21.4267535045 | 53.278867506 |
| 72.8904768723 | 78.5060631452 |
| 29.1788490089 | 86.6088161574 |
| 6.3161819599 | 52.3557279487 |
| 6.7368844987 | 84.0753619355 |
| 25.2622687939 | 21.8745250686 |
| 50.8433991824 | 54.1560703438 |
| 87.8995465788 | 82.5796499913 |
| 35.8752644678 | 52.1050378057 |
| 44.7089896654 | 8.1202036317 |
| 69.6525671545 | 78.9947245849 |
| 28.3228485441 | 79.8282514775 |
| 14.3904608861 | 49.8490626156 |
| 88.7766481936 | 96.5946095581 |
| 76.7931696157 | 6.8514962009 |
| 9.6768894925 | 57.8644055084 |
| 7.4591983077 | 77.9192795258 |
| 66.3769227285 | 8.8908166037 |
| 37.8425651262 | 72.9648048612 |
| 8.4812421396 | 15.4117534907 |
| 79.9637319868 | 44.9445422198 |
| 21.4818403025 | 94.2863110036 |
| 6.993066511 | 0.0389041396 |
| 3.2102547777 | 49.0448718854 |
| 90.8194866778 | 59.3113622616 |
| 18.0214715193 | 10.0044913456 |
| 75.2422052558 | 74.8305168929 |
| 31.6391047805 | 48.7807488394 |
